Real-Time Electricity Pricing
Monte Carlo Analysis of Real-Time Electricity Pricing for Connecticut Industrial Loads
Sean Edward Paquette
Rensselaer Polytechnic Institute – Hartford, Connecticut
MANE – 6960 (Mathematical Modeling of Energy & Environmental)
Professor Ernesto Gutierrez-Miravete, Ph.D.
Spring 2013
Abstract: In this paper, potential cost benefits for adopting a real-time pricing tariff is studied.
To simulate economic benefits a complete Monte Carlo Analysis was performed using 2013
historical locational marginal pricing data for sub-regional base and peak loading generators
located in a large transmission organization.
Keywords: Monte Carlo Analysis; Real-Time Pricing; Energy Tariffs; Economic Benefits; Returns
I. INTRODUCTION
Independent System Operator (ISO) New England is an independent Regional
Transmission Organization (RTO) and an electric industry leader controlling a competitive
wholesale Locational Marginal Pricing (LMP) based electricity market, managing highvoltage electricity in Connecticut, Massachusetts, Maine, Rhode Island, Vermont and New
Hampshire. Today, ISO New England operates a market with more than 400 companies
producing a generating capacity of 30,000 megawatts (MW) and delivering reliable power to
more than 6.5 million businesses and households. The analysis discussed in this paper can be
applied to any organization operating under the real-time LMP system. Specifically, to
illustrate potential industrial electricity cost savings, this paper uses data collected from
Connecticut generators located in the ISO New England Organization.
Generating units and loads in a real-time LMP based organization are paid based on
the locational marginal cost at their given load location. The locational prices are calculated
hourly reflecting the marginal cost of energy, marginal cost of losses and marginal cost of
congestion. Furthermore, the cheapest generating units in the organization may not always
be selected to supply the electricity demand due to transmission line capacities. The costs
associated with scheduling a generator out of order due to line capacities is called
transmission congestion costs. Electricity tariffs can protect against these volatile
transmission congestion costs.
This paper is organized as follows: Section 2 provides a detailed description of RealTime Pricing (RTP) tariffs. Section 3 summarizes the Monte Carlo Analysis of real-time
electricity pricing used in this report, followed by a summary of results in Section 4.
II. REAL-TIME PRICING TARIFF
RTP tariffs offer the customer the opportunity to purchase electricity for a set period of
time based on the present daily load demands and prices of the electricity market. RTP tariff
prices are derived based on the demand and hourly supply on the electricity grid and are
therefore very volatile. Fixed electricity tariffs force the customer to purchase electricity for a
set price. Tariffs must achieve two main objectives: first, [1] they must generate the income
required to cover all costs of supplying the electricity. Secondly, they must send the right
economic signals to each customer to ensure that they use the service in the most efficient
way, socio-economically speaking. There are over 70 U.S. utilities offering RTP tariff
programs. These programs help reduce price volatility and attempt to limit market power for
producing companies.
III. MONTE CARLO ANALYSIS
The analysis used in this study to determine potential economic benefits using a RTP
rate under different load parameters is called a Monte Carlo Analysis. Monte Carlo is a [2]
suite of methods which employ stochastic techniques to solve many-body quantum problems.
To evaluate the potential benefits of RTP tariffs electrical load representation are computed.
Due to the tremendous competition between utility companies across the United States
current electrical load data was not available. To model the industrial power demand, this
report uses the parameter values and probability distributions for load functions identified and
mathematically modeled using sinusoidal terms in Reference [2], Table 1.
Table 1. Parameter Values and Probability Distribution for Load Functions; Reference [2]; Appendix C
Figure 1. High & Low Load Factor Demands for One Week; Appendix D
Figure 1 illustrates industrial high and low load factors for a one week period. The
values in Figure 1 were calculated using data from Table 1, equations (1) and (2). Equation
(1) represents the high load factor industrial loads and equation (2) represents the low load
factors for industrial loads. Customers interested in potential seasonal, one-time event and
ramp up/down phases electricity cost savings through RTP tariffs can alter the below
equations to target the specific load cycle factor.
dH(nTm) = a1H * sin(2πf1nTm) + a2H * sin(2πf2nTm + ɸ2H + Ɛɸn) + dbaseH + Ɛbn
dL(nTm) = -a1L * dbase * sin(2πf1nTm + ɸ1L) + a2 * dbase * sin(2πf2nTm + ɸ2L + Ɛɸn) + dbaseL + Ɛbn
(1)
(2)
The analysis in this report used a one week real-time Connecticut LMP between
January 1, 2013 to January 7, 2013. Figure 2 illustrates the normalized electricity price. The
normalized electricity price is calculated by dividing the RTP series by the maximum RTP
for the given interval.
Figure 2. Connecticut Real-time Locational Marginal Prices; Appendix E
To calculate the normalized customer cost for fixed rate tariffs and RTP tariffs for a
one week interval, Connecticut RTP representing the supply/demand relationship was used.
The fixed rate electricity costs indexes are calculated using equations (3) and (4), while
equations (5) and (6) are used to compute electricity cost indexes for RTP tariffs.
Fixed Rate Electricity Cost Index (High Demand) = FECH = pnf Σ dh(n)
(3)
Fixed Rate Electricity Cost Index (Low Demand) = FECL = pnf Σ dL(n)
(4)
Real-Time Pricing Electricity Cost Index (High Demand) = RECH = Σ pnndh(n)
(5)
Real-Time Pricing Electricity Cost Index (Low Demand) = RECL = Σ pnndL(n)
(6)
To quantify and demonstrate potential customer savings a benefit index was graphed
(Figure 3) using computed data derived from equations (7) and (8). Figure (3) uses a fixed
rate (pnf) value used in the Reference [2] model. The benefit index is the difference between
the fixed electricity costs and the RTP costs for the high and low load demand. The benefit
index values will change depending on the customer’s location and power pattern selection.
Reference [2], when the index, B is zero, adopting the RTP tariff produces no additional
benefits over the fixed rate. If B is negative, then the electricity costs under the RTP tariff are
larger than the fixed rate, therefore, accepting the RTP rate is not cost effective for negative
values of the benefits index. If B is positive, then the cost of adopting the RTP rate structure
is less than the cost of the fixed rate, so a customer would realize savings by switching to the
RTP tariff.
BH = pnfΣdh(n) - Σpnndh(n)
(7)
BL = pnfΣdL(n) - ΣpnndL(n)
(8)
Figure 3. Benefit Index; Appendix F
Majority of the benefit index in Figure (3) is positive above the zero value.
Therefore, it is beneficial and profitable for the customer to adopt the RTP tariff structure.
IV. TEST
To test the model, Figure (4) used the Connecticut Light and Power Company large
time-of-day rate 57 (manufactures) as a fixed rate (pnf) value, Reference [3]. The fixed rate
value varied between $950.00/month for manufacturers requiring less than 2,000kW demand
and $4,000.00/month for manufactures with over a 5,000kW demand. As shown in Figure (4),
the bulk of the benefit index based on a model using Connecticut Light & Power fixed rate 57
is close to or below zero. Therefore, it is not cost effective for the customer to transition to a
RTP tariff.
Figure 4. Benefit Index _ Rate 57; Appendix G
This model allows customers to structure different scenarios to be analyzed using a
range of electricity loads and a collection of fixed rates specific to their geographic area to
maximize their economic potential if a RTP tariff is used.
APPENDIX
Appendix A: January 1, 2013 to March 31, 2013 data extracted for ISO New England
website. This file is hourly data containing loads, day-ahead and real-time prices for New
England
Appendix B:
Connecticut Light & Power, “Large Time-Of-Day Electric Service
(Manufacturers), Rate 57; Reference [3]
Appendix C: Enlarged Table 1. Parameter values and probability distribution for load
functions; Reference [2]
Appendix D: Enlarged Figure 1. High & Low Load Factor Demands for One Week
Appendix E: Enlarged Figure 2. Connecticut Real-time Locational Marginal Prices
Appendix F: Enlarged Figure 3. Benefit Index
Appendix G: Enlarged Figure 4. Benefit Index Using a CT Fixed Rate 57
REFERENCES
[1] J. Reneses, T. Gomez, J. Rivier, J. Angarita, “Electricity tariff design for transition economies, Application
to the Libyan power system,” Elsevier. Energy Economics. vol. 33, pp. 33–43, 2011.
[2] L. Mitas, “Quantum Monte Carlo,” Current Chemistry. Current Opinion in Solid State & Materials Science.
vol. 2, pp. 696–700, 1997.
[3] Connecticut Light & Power, “Large Time-Of-Day Electric Service (Manufacturers), Rate 57,” 2013.